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Course materials for 2020-11-2 AFEC at XTBG.

1 Prerequisites

Did you install picante and FD?

install.packages("picante")
install.packages("FD")

It’s better if you have those packages too.

install.packages("tidyverse")
install.packages("rmarkdown")
install.packages("DT")

Load pacakges.

library(picante)
library(FD)
library(tidyverse)
library(rmarkdown)

2 Data

2.1 Community

samp <- read_csv("./data/samp.csv")

DT::datatable(samp)
samp_mat <- as.matrix(samp[, -1])
rownames(samp_mat) <- samp$Site

samp_mat
##       Illicium_macranthum Manglietia_insignis Michelia_floribunda Beilschmiedia_robusta Neolitsea_chuii
## Site1                   1                   0                   0                     0               0
## Site2                   1                   2                   2                     2               0
## Site3                   1                   0                   0                     0               0
## Site4                   1                   1                   0                     0               0
## Site5                   1                   0                   0                     0               1
##       Lindera_thomsonii Actinodaphne_forrestii Machilus_yunnanensis
## Site1                 0                      0                    0
## Site2                 0                      0                    0
## Site3                 2                      2                    2
## Site4                 2                      2                    0
## Site5                 1                      0                    0

2.2 Phylogeny

phylo <- read.tree("./data/dummy_tree.newick")
plot(phylo)

2.3 Traits

Abbreviation Trait Unit
LMA Leaf mass per area g m-2
LL Leaf lifespans (longevity) months
Amass Maximum photosynthetic rates per unit mass nnoml g-1 s-1
Rmass Dark resperation rates per unit mass nnoml g-1 s-1
Nmass Leaf nitrogen per unit mass %
Pmass Leaf phosphorus per unit mass %
WD Wood density g cm-3
SM Seed dry mass mg 
trait <- read_csv("./data/dummy_trait.csv") 

# trait <- read.csv("./data/dummy_trait.csv") is fine too.

DT::datatable(trait)

2.4 Check the histograms of trait values first

trait_long <- trait %>%
  gather(trait, val, 2:9)

ggplot(trait_long, aes(x = val)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

Probably we can do log-transformation for all the traits except for WD.

trait2 <- trait %>%
  mutate(logLMA = log(LMA),
         logLL = log(LL),
         logAmass = log(Amass),
         logRmass = log(Rmass),
         logNmass = log(Nmass),
         logPmass = log(Pmass),
         logSM = log(SM)) %>%
  dplyr::select(sp, logLMA, logLL, logAmass, logRmass, logNmass, logPmass, WD, logSM)

DT::datatable(trait2)
trait2 %>%
  gather(trait, val, 2:9) %>%
  ggplot(., aes(x = val)) +
  geom_histogram(position = "identity") +
  facet_wrap(~ trait, scale = "free")

3 Fisrt-order metrics (without phylogeny or traits)

3.1 Species richness, Beta diversity metrics

Skip

3.2 Nonmetric Multidimensional Scaling (NMDS)

res_mds <- metaMDS(samp_mat)
## Run 0 stress 0 
## Run 1 stress 0.09681631 
## Run 2 stress 0.09681215 
## Run 3 stress 0 
## ... Procrustes: rmse 0.03863589  max resid 0.0534632 
## Run 4 stress 0.09680972 
## Run 5 stress 0 
## ... Procrustes: rmse 0.0511207  max resid 0.06633629 
## Run 6 stress 0.0968117 
## Run 7 stress 0 
## ... Procrustes: rmse 0.04197551  max resid 0.05283911 
## Run 8 stress 0.1302441 
## Run 9 stress 0 
## ... Procrustes: rmse 0.06395026  max resid 0.09776802 
## Run 10 stress 8.051887e-05 
## ... Procrustes: rmse 0.02885092  max resid 0.04086429 
## Run 11 stress 0.1302441 
## Run 12 stress 0 
## ... Procrustes: rmse 0.099269  max resid 0.149765 
## Run 13 stress 0.1302441 
## Run 14 stress 4.169502e-05 
## ... Procrustes: rmse 0.1262325  max resid 0.1954984 
## Run 15 stress 0 
## ... Procrustes: rmse 0.05931327  max resid 0.09237511 
## Run 16 stress 0 
## ... Procrustes: rmse 0.1053699  max resid 0.1813597 
## Run 17 stress 0 
## ... Procrustes: rmse 0.02327438  max resid 0.03516164 
## Run 18 stress 0.1302441 
## Run 19 stress 0 
## ... Procrustes: rmse 0.1092088  max resid 0.166231 
## Run 20 stress 0.09681431 
## *** No convergence -- monoMDS stopping criteria:
##     11: stress < smin
##      6: stress ratio > sratmax
##      3: scale factor of the gradient < sfgrmin
plot(res_mds)

We can use the function ordiplot and orditorp to add text to the plot in place of points to make some more sence.

ordiplot(res_mds, type = "n")
orditorp(res_mds,display="species",col="red",air=0.01)
orditorp(res_mds,display="sites",cex=1.25,air=0.01)

4 Phylogenetic metrics

4.1 Branch length based metric

4.1.1 PD

res_pd <- pd(samp_mat, phylo)

res_pd
##             PD SR
## Site1 1.000000  1
## Site2 3.022727  4
## Site3 2.909091  4
## Site4 3.136364  4
## Site5 2.454545  3

You can always see the help.

?pd

4.2 Distance based metric

cophenetic() creates distance matrices based on phylogenetic trees. Let’s see the first 5 species.

cophenetic(phylo)[1:5, 1:5]
##                     Acer_campbellii Melia_toosendan Skimmia_arborescens Rhus_sylvestris Sterculia_nobilis
## Acer_campbellii           0.0000000      0.18181818          0.18181818       0.3636364         0.5454545
## Melia_toosendan           0.1818182      0.00000000          0.09090909       0.3636364         0.5454545
## Skimmia_arborescens       0.1818182      0.09090909          0.00000000       0.3636364         0.5454545
## Rhus_sylvestris           0.3636364      0.36363636          0.36363636       0.0000000         0.5454545
## Sterculia_nobilis         0.5454545      0.54545455          0.54545455       0.5454545         0.0000000

4.2.1 MPD

\(MPD = \frac{1}{n} \Sigma^n_i \Sigma^n_j \delta_{i,j} \; i \neq j\), where \(\delta_{i, j}\) is the pairwised distance between species i and j

res_mpd <- mpd(samp_mat, cophenetic(phylo))

res_mpd
## [1]       NA 1.568182 1.454545 1.606061 1.636364

The above vector shows MPD for each site.

4.2.2 MNTD

\(MNTD = \frac{1}{n} \Sigma^n_i min \delta_{i,j} \; i \neq j\), where \(min \delta_{i, j}\) is the minimum distance between species i and all other species in the community.

res_mntd <- mntd(samp_mat, cophenetic(phylo))

res_mntd
## [1]       NA 1.181818 1.181818 1.295455 1.272727

5 Functional metrics

5.1 Community weighted means (CWM)

\[ CWM_i = \frac{\sum_{j=1}^n a_{ij} \times t_{j}}{\sum_{j=1}^n a_{ij}} \]

tmp <- trait2 %>%
  filter(sp %in% colnames(samp_mat)) 

tmp
## # A tibble: 8 x 9
##   sp                     logLMA logLL logAmass logRmass logNmass logPmass    WD   logSM
##   <chr>                   <dbl> <dbl>    <dbl>    <dbl>    <dbl>    <dbl> <dbl>   <dbl>
## 1 Actinodaphne_forrestii   4.24  2.53     5.01    2.17     0.412   -1.83   0.48  0.300 
## 2 Beilschmiedia_robusta    3.61  3.09     5.72    3.53     1.75    -1.35   0.47  0.770 
## 3 Illicium_macranthum      5.66  4.75     3.27    0.793   -0.288   -3.51   0.4  -0.0305
## 4 Lindera_thomsonii        4.47  3.70     5.49    3.02     0.626   -3.00   0.53 -0.734 
## 5 Machilus_yunnanensis     4.26  3.36     4.65    2.69     0.239   -0.821  0.59  0.0770
## 6 Manglietia_insignis      6.22  5.24     3.10    0.255   -0.431   -3.91   0.45 -0.0513
## 7 Michelia_floribunda      4.93  3.99     3.65    2.00     0.457   -3.91   0.54  0.621 
## 8 Neolitsea_chuii          4.65  4.18     5.20    2.30     0.489   -2.12   0.43 -1.71
(ab <- apply(samp_mat, 1, sum))
## Site1 Site2 Site3 Site4 Site5 
##     1     7     7     6     3
# inner product
(CWS <- samp_mat %*% as.matrix(tmp[,-1]))
##          logLMA     logLL  logAmass  logRmass  logNmass   logPmass   WD      logSM
## Site1  4.236712  2.527327  5.006359  2.173615 0.4121097  -1.832581 0.48  0.3001046
## Site2 31.729450 25.585161 33.973907 16.848875 4.5974297 -17.531309 3.28  0.3114643
## Site3 35.828159 29.342331 28.910240 11.266140 1.4425535 -21.721201 3.32 -1.9909259
## Site4 30.140733 24.069613 24.233478 10.201674 2.2197972 -18.827747 2.93  2.2087792
## Site5 14.713415 11.128090 12.759265  5.116104 0.2203436  -6.565585 1.52  0.3257723
(CWM <- CWS / ab)
##         logLMA    logLL logAmass logRmass   logNmass  logPmass        WD      logSM
## Site1 4.236712 2.527327 5.006359 2.173615 0.41210965 -1.832581 0.4800000  0.3001046
## Site2 4.532779 3.655023 4.853415 2.406982 0.65677568 -2.504473 0.4685714  0.0444949
## Site3 5.118308 4.191762 4.130034 1.609449 0.20607908 -3.103029 0.4742857 -0.2844180
## Site4 5.023456 4.011602 4.038913 1.700279 0.36996620 -3.137958 0.4883333  0.3681299
## Site5 4.904472 3.709363 4.253088 1.705368 0.07344788 -2.188528 0.5066667  0.1085908

5.2 Distance based metrics

5.2.1 Prepare a trait distance matrix

We have a data.fame of traits. First we need to prepare a trait matrix, then a distance matrix based on trait values.

trait_mat0 <- as.matrix(trait2[, -1])
rownames(trait_mat0) <- trait2$sp

Let’s see a subset of the trait matrix

trait_mat0[1:5, 1:5]
##                          logLMA    logLL logAmass logRmass  logNmass
## Acer_campbellii        3.684118 1.957274 6.892692 4.002047 1.8809906
## Actinodaphne_forrestii 4.236712 2.527327 5.006359 2.173615 0.4121097
## Alnus_nepalensis       4.743366 4.010419 4.341335 2.022871 0.5007753
## Anneslea_fragrans      4.190715 3.293241 5.162211 3.703522 1.4632554
## Beilschmiedia_robusta  3.614964 3.085573 5.722441 3.526655 1.7544037

Then, we will make trait distance matrix based on the Euclidean distance. There are other distance measures, for example Gower’s Distance, but we focus on the Euclidean distance today.

Before calulating distance, we need to make sure unit change in ditances have same for different traits. We will scale trait values so that then have mean = 0 and SD = 1. (e.g., \((X_i - \mu) / \sigma\))

trait_mat <- scale(trait_mat0)

par(mfrow = c(2, 2))
hist(trait_mat0[, "logLMA"])
hist(trait_mat[, "logLMA"])
hist(trait_mat0[, "WD"])
hist(trait_mat[, "WD"])

par(mfrow = c(1, 1))

Now we can make a trait distance matirx.

trait_dm <- as.matrix(dist(trait_mat))

Let’s see the first 5 species.

trait_dm[1:5, 1:5]
##                        Acer_campbellii Actinodaphne_forrestii Alnus_nepalensis Anneslea_fragrans Beilschmiedia_robusta
## Acer_campbellii               0.000000               3.799360         5.216902          3.175911              2.545269
## Actinodaphne_forrestii        3.799360               0.000000         2.415031          2.335392              2.565063
## Alnus_nepalensis              5.216902               2.415031         0.000000          3.225141              3.638183
## Anneslea_fragrans             3.175911               2.335392         3.225141          0.000000              1.579930
## Beilschmiedia_robusta         2.545269               2.565063         3.638183          1.579930              0.000000

5.2.2 MPD

mpd(samp_mat, trait_dm)
## [1]       NA 4.288349 3.530805 3.961248 3.438008
ses.mpd(samp_mat, trait_dm)
##       ntaxa  mpd.obs mpd.rand.mean mpd.rand.sd mpd.obs.rank  mpd.obs.z mpd.obs.p runs
## Site1     1       NA           NaN          NA           NA         NA        NA  999
## Site2     4 4.288349      3.687304   0.8003616          784  0.7509671     0.784  999
## Site3     4 3.530805      3.747481   0.8124123          454 -0.2667075     0.454  999
## Site4     4 3.961248      3.734575   0.8142402          637  0.2783864     0.637  999
## Site5     3 3.438008      3.706005   0.9939952          433 -0.2696156     0.433  999

5.2.3 MNTD

mntd(samp_mat, trait_dm)
## [1]       NA 2.504352 2.697074 1.873825 2.613585

5.3 Branch length based metric

5.3.1 FD

We will make a functional dendrogram using clustring methods. We use UPGMA in this example.

t_clust <- hclust(dist(trait_mat), method = "average")

plot(t_clust)

5.3.2 More functional diversity metrics

res_fd <- dbFD(trait_mat[colnames(samp_mat), ], samp_mat)
## FEVe: Could not be calculated for communities with <3 functionally singular species. 
## FDis: Equals 0 in communities with only one functionally singular species. 
## FRic: To respect s > t, FRic could not be calculated for communities with <3 functionally singular species. 
## FRic: Dimensionality reduction was required. The last 5 PCoA axes (out of 7 in total) were removed. 
## FRic: Quality of the reduced-space representation = 0.811349 
## FDiv: Could not be calculated for communities with <3 functionally singular species.
res_fd
## $nbsp
## Site1 Site2 Site3 Site4 Site5 
##     1     4     4     4     3 
## 
## $sing.sp
## Site1 Site2 Site3 Site4 Site5 
##     1     4     4     4     3 
## 
## $FRic
##    Site1    Site2    Site3    Site4    Site5 
##       NA 5.453089 2.917904 3.000656 3.553247 
## 
## $qual.FRic
## [1] 0.811349
## 
## $FEve
##     Site1     Site2     Site3     Site4     Site5 
##        NA 0.7595456 0.6769400 0.7085376 0.7584941 
## 
## $FDiv
##     Site1     Site2     Site3     Site4     Site5 
##        NA 0.7301943 0.7617251 0.9166699 0.8261683 
## 
## $FDis
##    Site1    Site2    Site3    Site4    Site5 
## 0.000000 2.710994 1.842262 2.311159 2.042416 
## 
## $RaoQ
##    Site1    Site2    Site3    Site4    Site5 
## 0.000000 8.376023 4.005094 5.664467 4.379844 
## 
## $CWM
##           logLMA       logLL    logAmass   logRmass    logNmass   logPmass         WD      logSM
## Site1  1.4467783  1.17548950 -1.38976382 -1.9975087 -0.88119735 -1.2775781 -1.0150179 -0.2191496
## Site2  0.5666449  0.55085046 -0.56218769 -0.8908026 -0.09004842 -0.8660119 -0.2744691  0.1665816
## Site3 -0.1410729 -0.33319385  0.27087040 -0.2062427 -0.24084641  0.2088166  0.1242879 -0.2907346
## Site4  0.3670613  0.03104745  0.01551229 -0.7298853 -0.34295985 -0.5718506 -0.2341187 -0.3397288
## Site5  0.4305791  0.56352114  0.11718014 -0.5812855 -0.29128834 -0.6020974 -0.4833418 -0.9701997

7 Computing Environment

devtools::session_info()
## ─ Session info ───────────────────────────────────────────────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.2 (2020-06-22)
##  os       Manjaro Linux               
##  system   x86_64, linux-gnu           
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Asia/Shanghai               
##  date     2020-11-05                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────────────────────────────────────────────
##  package     * version date       lib source        
##  abind         1.4-5   2016-07-21 [1] CRAN (R 4.0.0)
##  ade4        * 1.7-15  2020-02-13 [1] CRAN (R 4.0.0)
##  ape         * 5.4-1   2020-08-13 [1] CRAN (R 4.0.2)
##  assertthat    0.2.1   2019-03-21 [1] CRAN (R 4.0.0)
##  backports     1.1.10  2020-09-15 [1] CRAN (R 4.0.2)
##  blob          1.2.1   2020-01-20 [1] CRAN (R 4.0.0)
##  broom         0.7.0   2020-07-09 [1] CRAN (R 4.0.2)
##  callr         3.4.4   2020-09-07 [1] CRAN (R 4.0.2)
##  cellranger    1.1.0   2016-07-27 [1] CRAN (R 4.0.0)
##  cli           2.0.2   2020-02-28 [1] CRAN (R 4.0.0)
##  cluster       2.1.0   2019-06-19 [1] CRAN (R 4.0.0)
##  colorspace    1.4-1   2019-03-18 [1] CRAN (R 4.0.0)
##  crayon        1.3.4   2017-09-16 [1] CRAN (R 4.0.0)
##  crosstalk     1.1.0.1 2020-03-13 [1] CRAN (R 4.0.0)
##  DBI           1.1.0   2019-12-15 [1] CRAN (R 4.0.0)
##  dbplyr        1.4.4   2020-05-27 [1] CRAN (R 4.0.2)
##  desc          1.2.0   2018-05-01 [1] CRAN (R 4.0.0)
##  devtools      2.3.2   2020-09-18 [1] CRAN (R 4.0.2)
##  digest        0.6.25  2020-02-23 [1] CRAN (R 4.0.0)
##  dplyr       * 1.0.2   2020-08-18 [1] CRAN (R 4.0.2)
##  DT            0.15    2020-08-05 [1] CRAN (R 4.0.2)
##  ellipsis      0.3.1   2020-05-15 [1] CRAN (R 4.0.2)
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##  farver        2.0.3   2020-01-16 [1] CRAN (R 4.0.0)
##  FD          * 1.0-12  2014-08-19 [1] CRAN (R 4.0.0)
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##  fs            1.5.0   2020-07-31 [1] CRAN (R 4.0.2)
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##  geometry    * 0.4.5   2019-12-04 [1] CRAN (R 4.0.0)
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##  sessioninfo   1.1.1   2018-11-05 [1] CRAN (R 4.0.0)
##  stringi       1.4.6   2020-02-17 [1] CRAN (R 4.0.0)
##  stringr     * 1.4.0   2019-02-10 [1] CRAN (R 4.0.0)
##  testthat      2.3.2   2020-03-02 [1] CRAN (R 4.0.0)
##  tibble      * 3.0.3   2020-07-10 [1] CRAN (R 4.0.2)
##  tidyr       * 1.1.1   2020-07-31 [1] CRAN (R 4.0.2)
##  tidyselect    1.1.0   2020-05-11 [1] CRAN (R 4.0.2)
##  tidyverse   * 1.3.0   2019-11-21 [1] CRAN (R 4.0.0)
##  usethis       1.6.3   2020-09-17 [1] CRAN (R 4.0.2)
##  utf8          1.1.4   2018-05-24 [1] CRAN (R 4.0.0)
##  vctrs         0.3.2   2020-07-15 [1] CRAN (R 4.0.2)
##  vegan       * 2.5-6   2019-09-01 [1] CRAN (R 4.0.0)
##  withr         2.3.0   2020-09-22 [1] CRAN (R 4.0.2)
##  xfun          0.16    2020-07-24 [1] CRAN (R 4.0.2)
##  xml2          1.3.2   2020-04-23 [1] CRAN (R 4.0.0)
##  yaml          2.2.1   2020-02-01 [1] CRAN (R 4.0.0)
## 
## [1] /home/mattocci/R/x86_64-pc-linux-gnu-library/4.0
## [2] /usr/lib/R/library